Aberystwyth. National Library of Wales. Lived there for 8+ years. Lots of walks. Coast. Not far from Aberaeron (honey ice-cream and good fish and chips) and on to New Quay (south) though the walk from the car park at the top from the beach is STEEP! Llanilar has an old Mansion on the road towards Tregaron. There's a lovely lake (name escapes me) through Penrhyncoch up a road, up a narrower road and beyond - at the right time one can pick bilberries. Red kites everywhere. Pony trekking.
Borth and Ynylas Dunes: opposite Aberdovey: for a day. Machynlleth along the Dovey for antiques and history. Further round, Aberdovey and Barmouth for a day.
Bow Street is where the 'runners' had their Quarterly Assizes. Have a look at the Tourist Information on-line for places of interest.